CvMcens: Cramér-von Mises test for complete and right-censored data

In GofCens: Goodness-of-Fit Methods for Right-Censored Data

Cramér-von Mises test for complete and right-censored data

Description

Function CvMcens computes the Cramér-von Mises test statistic and p-value for right-censored data against eight possible predefined or user-specified distributions using bootstrapping. This function also accounts for complete data.

Usage

## Default S3 method:
CvMcens(times, cens = rep(1, length(times)),
        distr = c("exponential", "gumbel", "weibull", "normal",
                  "lognormal", "logistic", "loglogistic", "beta"),
        betaLimits = c(0, 1), igumb = c(10, 10), BS = 999,
        params0 = list(shape = NULL, shape2 = NULL,
                       location = NULL, scale = NULL, theta = NULL),
        tol = 1e-04, start = NULL, ...)
## S3 method for class 'formula'
CvMcens(formula, data, ...)

Arguments

times	Numeric vector of times until the event of interest.
cens	Status indicator (1, exact time; 0, right-censored time). If not provided, all times are assumed to be exact.
distr	A string specifying the name of the distribution to be studied. The possible distributions are the exponential ("exponential"), the Weibull ("weibull"), the Gumbel ("gumbel"), the normal ("normal"), the lognormal ("lognormal"), the logistic ("logistic"), the loglogistic ("loglogistic"), and the beta ("beta") distribution. In addition, if the character string used is "name", every distribution for which the corresponding density (dname), distribution (pname), and random generator (rname) functions are defined, can be used.
betaLimits	Two-components vector with the lower and upper bounds of the Beta distribution. This argument is only required, if the beta distribution is considered.
igumb	Two-components vector with the initial values for the estimation of the Gumbel distribution parameters.
BS	Number of bootstrap samples.
params0	List specifying the parameters of the theoretical distribution. By default, parameters are set to NULL and estimated with the maximum likelihood method. This argument is only considered, if all parameters of the studied distribution are specified.
tol	Precision of survival times.
formula	A formula with a numeric vector as response (which assumes no censoring) or Surv object.
data	Data frame for variables in formula.
start	A named list giving the initial values of parameters of the named distribution or a function of data computing initial values and returning a named list. This argument may be omitted (default) for the eight prespecified distributions. See more details in mledist.
...	Additional arguments for the boot function of the boot package.

Details

Koziol and Green (1976) proposed a Cramér-von Mises statistic for randomly censored data. This function reproduces this test for a given survival data and a theorical distribution. In presence of ties, different authors provide slightly different definitions of the product-limit estimator, what might provide different values of the test statistic.

The parameter estimation is acomplished with the fitdistcens function of the fitdistrplus package.

To avoid long computation times due to bootstrapping, an alternative with complete data is the function cvm.test of the goftest package.

The precision of the survival times is important mainly in the data generation step of the bootstrap samples.

Value

CvMcens returns an object of class "CvMcens".

An object of class "CvMcens" is a list containing the following components:

Distribution	Null distribution.
Hypothesis	Parameters under the null hypothesis (if params0 is provided).
Test	Vector containing the value of the Cramér-von Mises statistic (CvM) and the estimated p-value (p-value).
Estimates	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
StdErrors	Vector containing the estimated standard errors.
aic	The Akaike information criterion.
bic	The so-called BIC or SBC (Schwarz Bayesian criterion).
BS	The number of bootstrap samples used.

Warning

If the amount of data is large, the execution time of the function can be elevated. The parameter BS can limit the number of random censored samples generated and reduce the execution time.

Author(s)

K. Langohr, M. Besalú, M. Francisco, A. Garcia, G. Gómez.

References

J. A. Koziol and S. B. Green. A Cramér-von Mises statistic for randomly censored data. In: Biometrika, 63 (3) (1976), 465-474. URL: https://doi.org/10.1093/biomet/63.3.465

A. N. Pettitt and M. A. Stephens. Modified Cramér-von Mises statistics for censored data. In: Biometrika, 63 (2) (1976), 291-298. URL: https://doi.org/10.1093/biomet/63.2.291

See Also

Function cvm.test (Package goftest) for complete data and gofcens for statistics and p-value of Kolmogorov-Smirnov, Cramér von-Mises and Anderson-Darling together for right-censored data.

Examples

# Complete data
set.seed(123)
CvMcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
        BS = 199)
summary(CvMcens(times = rweibull(100, 12, scale = 4), distr = "normal",
        BS = 99), degs = 4, print.AIC = FALSE, print.BIC = FALSE)

## Not run: 
# Censored data
set.seed(123)
colonsamp <- colon[sample(nrow(colon), 300), ]
CvMcens(Surv(time, status) ~ 1, colonsamp, distr = "normal")

## End(Not run)

GofCens documentation built on June 8, 2025, 10:11 a.m.